04984nam 22015255 450 991015475090332120190708092533.01-4008-8200-110.1515/9781400882007(CKB)3710000000620168(MiAaPQ)EBC4738781(DE-B1597)467917(OCoLC)979728674(DE-B1597)9781400882007(EXLCZ)99371000000062016820190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierTheory of Formal Systems. (AM-47), Volume 47 /Raymond M. SmullyanPrinceton, NJ : Princeton University Press, [2016]©19611 online resource (157 pages) illustrationsAnnals of Mathematics Studies ;301"A revision of the author's recent doctoral dissertation--[Princeton]."0-691-08047-X Includes bibliography.Frontmatter -- TABLE OF CONTENTS -- PREFACE -- ANNALS OF MATHEMATICS STUDIES -- CHAPTER I: FORMAL MATHEMATICAL SYSTEMS -- CHAPTER II: FORMAL REPRESENTABILITY AND RECURSIVE ENUMERABILITY -- CHAPTER III: INCOMPLETENESS -AND UNDECIDABILITY -- CHAPTER IV: RECURSIVE FUNCTION THEORY -- CHAPTER V: CREATIVITY AND EFFECTIVE INSEPARABILITY -- SUPPLEMENT: APPLICATIONS TO MATHEMATICAL LOGIC -- REFERENCE AND BRIEF BIBLIOGRAPHYThis book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.Annals of mathematics studies ;no. 47.Recursive functionsMetamathematicsAddition.Algebraic geometry.Alonzo Church.Arithmetic function.Arithmetic.Atomic sentence.Axiom A.Axiom schema.Axiom.Axiomatic system.Binary relation.Cantor's diagonal argument.Cartesian product.Characterization (mathematics).Chinese remainder theorem.Closed-form expression.Closure (mathematics).Combination.Combinatory logic.Complement (set theory).Concatenation theory.Consistency.Constructive proof.Corollary.Countable set.Counterexample.Decidability (logic).Decision problem.Definable set.Diagonalization.Direct proof.Disjoint sets.Enumeration.Equation.Existential quantification.Exponential function.Finite set.Formal system.Functional calculus.Gödel numbering.Gödel's incompleteness theorems.Herbrand's theorem.Inference.Integer factorization.Iteration.John Myhill.Logical connective.Logical consequence.Mathematical induction.Mathematical logic.Mathematician.Mathematics.Metamathematics.Modus ponens.Natural number.Negation.Number theory.Order theory.Parity (mathematics).Peano axioms.Predicate (mathematical logic).Prenex normal form.Primitive recursive function.Quantifier (logic).Recursion.Recursive set.Recursively enumerable set.Remainder.Requirement.Rule of inference.Scientific notation.Sequence.Set (mathematics).Sign (mathematics).Special case.Subset.Suggestion.System U.Theorem.Theory.Transfinite number.Turing machine.Universal set.Validity.Variable (mathematics).Zermelo set theory.Recursive functions.Metamathematics.511.33Smullyan Raymond M., 50650DE-B1597DE-B1597BOOK9910154750903321Theory of Formal Systems. (AM-47), Volume 472788798UNINA